Q T2.8. The distribution of the time it ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 2: Q T2.8. (page 149)

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right with a mean of $30$ minutes and a standard deviation of $15$ minutes. The distribution of $z -$ scores for those times is
a. Normally distributed with mean $30$ and SD $15$
b. skewed to the right with a mean $30$ and SD $15$
c. Normally distributed with mean $0$ and SD $1$
d. skewed to the right with mean $0$ and SD $1$
e. skewed to the right, but the mean and standard deviation cannot be determined without more information.

Short Answer

Expert verified

The correct option is (d) skewed to the right with mean $0$ and SD $1$

Step by step solution

Given information

With a mean of 30 minutes and a standard deviation of 15 minutes, the distribution of how long it takes different people to complete a crossword puzzle is highly skewed to the right.

Explanation

With a mean of $30$ minutes and a standard deviation of $15$ minutes, the population distribution would be biased to the right. The shape of the $z -$ score distribution is always the same as the shape of the population distribution, indicating that the $z -$ scores have a right $-$ skewed distribution.

However, because $z -$ scores are the standardized form of data values, they always have a mean of zero and a standard deviation of one.

Hence, the correct option is (d)